Guzman, a minister since late 2019 and a close ally of President Alberto Fernandez, posted a letter on Twitter announcing his decision, adding he maintained "confidence in my vision of the path Argentina should follow."
The centre-left Peronist president is facing his lowest approval rating since taking office in 2019, with cracks in his coalition, inflation running above 60%, the peso currency under growing pressure and sovereign bonds at record lows.
Guzman, a moderate, had clashed with powerful Vice President Cristina Fernandez de Kirchner, a militant two-term former president, who has criticised his handling of the economy and called for greater spending to alleviate high poverty levels.
The resignation leaves the ministry leaderless just as Guzman was expected to travel to Europe to negotiate a $2 billion debt deal with the Paris Club of sovereign lenders. It also deals a blow to Fernandez's weakening power base.
"It is the chronicle of a death foretold," said Mariel Fornoni, director of the Management and Fit consultancy, adding that a painful loss in midterm elections last year for the government had hurt President Fernandez badly.
"Now he has lost another piece of his board, perhaps the most important, and is increasingly alone."
Investors, already jittery about the country's economic outlook, have pushed bonds down toward 20 cents on the dollar in recent weeks. All eyes now will be on Guzman's replacement.
Guzman, 39, said "there should be a political agreement within the governing coalition" to choose his successor.
The president's office said that it did not yet know when a replacement for Guzman would be announced. Fernandez had summoned members of his Cabinet and allies to an emergency meeting, one government source said.
"The president deeply regrets the decision but respects it. He is analysing his next decisions," said another government source with knowledge of the matter.
Two Economy Ministry officials, asking not to be named, said that Guzman's position had become untenable, especially without support for his economic agenda.
"He couldn't continue without the tools and with (Vice President) Cristina (Fernandez de Kirchner) against him," one of the two people said. "When things are no longer possible, it is an act of responsibility to leave."
Guzman tellingly posted his resignation letter while Fernandez de Kirchner was giving a speech commemorating iconic former Argentine President Juan Domingo Peron.
Miguel Kiguel, former secretary of finance in Argentina, told Reuters that whoever takes over will have a tough time, noting that inflation could hit 80% this year and there is a gap of nearly 100% between official and parallel exchange rates.
"We don't know who's coming, but this will be a very hot potato," Kiguel said. "Whoever comes is going to have a very complicated time."
Guzman was the driving force in sealing a new $44 billion deal with the IMF earlier this year to replace a failed program from 2018. However, he was unable to tamp down sky-high inflation, exacerbated by the war in Ukraine, while soaring energy import costs have hit the country's currency reserves.